Global existence and boundedness of solutions in a reaction-diffusion system of Michaelis-Menten-type predator-prey model with nonlinear prey-taxis and random diffusion

This article deals with a 2 ? reaction-diffusion-taxis model consisting of Michaelis-Menten functional response predator-prey system. The critical section this is that temporal-spatial evolution the predators? velocity depends largely on gradient prey. But beyond that, system also inscribes prey-taxis mechanism an immediate movement predator u in to change prey v (which leads collection u). By using contraction mapping principle, Lp estimates and Schauder parabolic equations, we prove global existence uniqueness classical solutions model. In addition this, boundedness by overcome difficulties brought nonlinear prey-taxis.